1
2/* @(#)s_tanh.c 1.3 95/01/18 */
3/*
4 * ====================================================
5 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
6 *
7 * Developed at SunSoft, a Sun Microsystems, Inc. business.
8 * Permission to use, copy, modify, and distribute this
9 * software is freely granted, provided that this notice
10 * is preserved.
11 * ====================================================
12 */
13
14/* Tanh(x)
15 * Return the Hyperbolic Tangent of x
16 *
17 * Method :
18 *				       x    -x
19 *				      e  - e
20 *	0. ieee_tanh(x) is defined to be -----------
21 *				       x    -x
22 *				      e  + e
23 *	1. reduce x to non-negative by ieee_tanh(-x) = -ieee_tanh(x).
24 *	2.  0      <= x <= 2**-55 : ieee_tanh(x) := x*(one+x)
25 *					        -t
26 *	    2**-55 <  x <=  1     : ieee_tanh(x) := -----; t = ieee_expm1(-2x)
27 *					       t + 2
28 *						     2
29 *	    1      <= x <=  22.0  : ieee_tanh(x) := 1-  ----- ; t=ieee_expm1(2x)
30 *						   t + 2
31 *	    22.0   <  x <= INF    : ieee_tanh(x) := 1.
32 *
33 * Special cases:
34 *	tanh(NaN) is NaN;
35 *	only ieee_tanh(0)=0 is exact for finite argument.
36 */
37
38#include "fdlibm.h"
39
40#ifdef __STDC__
41static const double one=1.0, two=2.0, tiny = 1.0e-300;
42#else
43static double one=1.0, two=2.0, tiny = 1.0e-300;
44#endif
45
46#ifdef __STDC__
47	double ieee_tanh(double x)
48#else
49	double ieee_tanh(x)
50	double x;
51#endif
52{
53	double t,z;
54	int jx,ix;
55
56    /* High word of |x|. */
57	jx = __HI(x);
58	ix = jx&0x7fffffff;
59
60    /* x is INF or NaN */
61	if(ix>=0x7ff00000) {
62	    if (jx>=0) return one/x+one;    /* ieee_tanh(+-inf)=+-1 */
63	    else       return one/x-one;    /* ieee_tanh(NaN) = NaN */
64	}
65
66    /* |x| < 22 */
67	if (ix < 0x40360000) {		/* |x|<22 */
68	    if (ix<0x3c800000) 		/* |x|<2**-55 */
69		return x*(one+x);    	/* ieee_tanh(small) = small */
70	    if (ix>=0x3ff00000) {	/* |x|>=1  */
71		t = ieee_expm1(two*ieee_fabs(x));
72		z = one - two/(t+two);
73	    } else {
74	        t = ieee_expm1(-two*ieee_fabs(x));
75	        z= -t/(t+two);
76	    }
77    /* |x| > 22, return +-1 */
78	} else {
79	    z = one - tiny;		/* raised inexact flag */
80	}
81	return (jx>=0)? z: -z;
82}
83